On Recursively Unsolvable Problems in Topology and Their Classification

Publisher Summary This chapter discusses recursively unsolvable problems in topology and their classification. The decision problems that have been considered, pertain to diffeomorphism homeomorphism, combinatorial equivalence, and homotopy equivalence. For each dimension n ≥4 and for each recursively enumerable degree of unsolvability D , there exists a recursive class C ( n , D ) of finite presentations of n -manifolds, endowed with a differentiable and a compatible combinatorial structure. The chapter discusses a topological analogue of the Markov–Addison–Feeney–Adjan–Rabin theorem.

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